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PART I: SYMPLECTIC MANIFOLDS 1. Symplectic Forms and Linear Algebra 2. Symplectic Form on the Cotangent Bundle PART II: SYMPLECTOMORPHISMS 3. Lagrangian Submanifolds 4. Generating Functions 5. Poincaré Recurrence Theorem PART III: LOCAL FORMS 6. Preparation for Local Theory 7. Moser Theorems 8. Darboux–Moser–Weinstein Theory 9. Weinstein Tubular Neighborhood Theorem PART IV: CONTACT MANIFOLDS 10. Contact Forms and Distribution 11. Contact Dynamics and Reeb Vector Fields PART V: COMPATIBLE ALMOST COMPLEX STRUCTURES 12. Almost Complex Structures 13. Compatible Triples 14. Dolbeault Theory PART VI: KÄHLER MANIFOLDS 15. Complex Manifolds 16. Kähler Forms and Metrics 17. Compact Kähler Manifolds PART VII: HAMILTONIAN MECHANICS 18. Hamiltonian Vector Fields 19. Variational Principles 20. Legendre Transform PART VIII: MOMENT MAPS 21. Lie Group Actions 22. Hamiltonian Actions PART IX: SYMPLECTIC REDUCTION 23. The Marsden–Weinstein–Meyer Theorem 24. Symplectic Reduction Technique PART X: MOMENT MAPS REVISITED 25. Moment Map in Gauge Theory 26. Existence and Uniqueness of Moment Maps 27. Convexity Properties PART XI: SYMPLECTIC TORIC MANIFOLDS 28. Classification of Symplectic Toric Manifolds 29. Delzant Construction 30. Duistermaat–Heckman Theorems
Lectures on Symplectic Geometry by Ana Cannas da Silva offers an elegant and accessible entry point into modern symplectic topology and geometric mechanics. Accessing this cannas da silva symplectic geometry pdf enables mathematicians, topologists, and theoretical physicists to explore Darboux's theorem, cotangent bundles, and contact structures. The volume comprehensively covers Poisson brackets, Lie group actions, symplectic reduction, momentum maps, and Delzant's theorem on toric manifolds. Studying this indispensable lectures on symplectic geometry book equips graduate students with vital tools for research in geometric quantization and Hamiltonian dynamics. Available as an open academic download lectures on symplectic geometry pdf download, this classic reference remains a gold standard textbook for advanced courses in differential geometry and topology.
Title: Lectures on Symplectic Geometry by Ana Cannas da Silva Publisher: Springer Year: 2006 Pages: 225 Type: PDF Language: English ISBN-10 #: 3540421955 ISBN-13 #: 978-3540421955 License: External Educational Resource Amazon: Amazon
The author Ana Cannas da Silva is a distinguished Portuguese mathematician and Senior Scientist at ETH Zürich, recognized globally for her expertise in symplectic geometry, geometric topology, and toric manifolds. Renowned for her exceptional pedagogical clarity, her textbook Lectures on Symplectic Geometry by Ana Cannas da Silva is widely adopted in graduate mathematics programs around the world.
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